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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 694 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  2. 2.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 48 (c) 56 (d) 38
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 5 (c) 4 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 18 (b) 19 (c) 9 (d) 20
  7. 7.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 300 (c) 343 (d) 333
  8. 8.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 6 (d) 5
  10. 10.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 444 (c) 453 (d) 374
  11. 11.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 45 (d) 15
  12. 12.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 14 (c) 42 (d) 126
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  14. 14.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 50 (c) 41 (d) 42
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 5 (b) 4 (c) 6 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  18. 18.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 478 (c) 390 (d) 477
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  20. 20.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 69 (c) 198 (d) 66
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 6 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  24. 24.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 540 (c) 432 (d) 531
  25. 25.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 40 (c) 50 (d) 49
  26. 26.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 104 (c) 122 (d) 114
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 8 (b) 13 (c) 10 (d) 12
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 18 (d) 7
  29. 29.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 54 (c) 153 (d) 51
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 19 (d) 8
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 12 (b) 4 (c) 10 (d) 11
  32. 32.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 312 (c) 303 (d) 280
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 16 (c) 15 (d) 14
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 17 (b) 16 (c) 18 (d) 6
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 21 (b) 20 (c) 19 (d) 9
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 16 (d) 17
  39. 39.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 19 (c) 60 (d) 57
  40. 40.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 62 (c) 70 (d) 52

Answer key

  1. 7
  2. 47
  3. 4
  4. 6
  5. 4
  6. 19
  7. 342
  8. 9
  9. 6
  10. 453
  11. 15
  12. 42
  13. 2
  14. 41
  15. 8
  16. 5
  17. 7
  18. 477
  19. 8
  20. 66
  21. 5
  22. 2
  23. 4
  24. 540
  25. 49
  26. 113
  27. 12
  28. 18
  29. 51
  30. 19
  31. 11
  32. 312
  33. 9
  34. 3
  35. 15
  36. 17
  37. 20
  38. 16
  39. 57
  40. 61

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